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Math on Widow Mines -- How STLife Dodged the Shots

Forum Index > StarCraft 2 Strategy
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Lone
Profile Joined August 2010
7 Posts
Last Edited: 2013-03-20 21:50:40
March 19 2013 13:17 GMT
#1
Hi everyone!

Sorry if this is in the wrong section, I fit it as best as I could. I'm pretty new here.
Anyways, I'm a regular over on the Bnet forums, and recently I posted some calculations I had on widow mines. However, being the Bnet forums, it was largely ignored, despite having significant merit and getting claim from the few people who did respond.

This is a primarily math based post, so bear with me.

Here's my transplanted post.

This little tidbit came to my attention during the recent MLG, and I decided to try to crunch some numbers in order to fully understand what it means in terms of gameplay.
I noticed in particular during Flash vs Life that Life was able to run through a number of Flash's minefields while only taking a few shots, far fewer than he should have.

The Theory:
Essentially, units are able to run through widow mine's attack radius without activating them due to the 1.5 second delay on the widow mine's activation.
After a unit leaves the mine's radius without activating the mine, the mine chooses a new target and attempts to "lock on" to that unit. It repeats until it finally locks on and fires.

So, widow mines have a lower "effective radius" than actual radius.

The Math:
I based my calculations on chord lengths using the following formula:
Chord Length = C = 2sqrt((r^2)-(d^2))
I then solved for d, getting:
d = sqrt((r^2)-(C/2)^2),

Which we can plug r=5 into, so my final formula became:

d = sqrt(25-(C/2)^2),
Where:
d = distance to Mine at closest point on chord (AKA Effective Radius)
C = unit speed*1.5.


Unit speed is calculated as range units traveled over 1 ingame second. So if you take your unit speed and multiply it by 1.5, you get the distance a unit can travel within a widow mine radius before activating the mine.

I bolded d because it's the most important, as we'll see soon.

For example, if we take Speedlings on creep, which have a C value of 9.163, we can do the following:
sqrt(25-(9.163/2)^2) = 2.002, or just 2.
This means that speedlings must travel on a chord which comes within 2 range of the widow mine in order to activate it before exiting the mine's range.

What this means in terms of Gameplay:
I hope that by now you're starting to understand what I'm getting at...

Based on the speed of the unit traveling over the mine, a mine has a radius in which the unit must pass in order for the mine to activate. I dubbed this radius "effective radius"

Let's again look at Zerglings, which have an above calculated d value of 2.
What that value means is that a speedling on creep, when traveling in a straight line through a mine's radius, must pass within 2 range of the mine in order to activate it.

And this is why Life was able to seemingly magically take Zero damage from mines. He likely realized, consciously or subconsciously, that if he attacked with the proper formation and using a move command, he could get mines to lock onto Zerglings which would not pass within 2 range of the burrowed mines. Once the first wave passed, the mines attempt to lock onto units based on proximity, so the chances of one locking onto a Zergling which just entered it's radius were near minimal. That led to a cascading "mine confusion" where they could not lock onto any unit for long enough to activate. More on this in the below bolded section.

Other unit examples: (All values in effective widow mine ranges):
+ Show Spoiler +
Mutalisks: 4.0
SpeedBanes on creep: 4.1
Speedlings off of creep: 3.5
Speedbanes off of creep: 4.5
Roaches W/Glial on creep: 4.1
Roaches w/Glial off creep: 4.4

Charging Chargelot: 2.1
Phoenix: 3.85

Hellion: 3.85
Stimmed units: 4.3


And here's a picture representation of the idea:
[image loading]

It's not a lot of leeway for most units, but speedlings, mutalisks and banelings are very able to run right over minefields without taking many, if any, hits for this very reason.
Furthermore, as pointed out by Terranic, once the first wave gets through the mines, the mine will start to select units based on proximity.
Given that, the very close units will already be halfway over the mine's radius. Meaning that they need to travel 5 range units in 1.5 seconds, which nearly all of the above mentioned units are able to do.
Any unit then traveling over the mine with a speed of at least 3.33(...) will be able escape the mine prior to activation, creating a cascading effect in which the mine is never able to activate and instead repeatedly changes targets.


Here's a graphic of this vital idea:
+ Show Spoiler +
[image loading]

- Credit to Mitosis for this excellent graphic!
And another:
+ Show Spoiler +
[image loading]

- Credit to Ahli for another sweet graphic, and Prplppleatr for analyzing it!

Of course, all of this only applies to units traveling in a straight line over the mine. However, this is relatively simple to do, as a move command will achieve this effect.

Conclusion:
Properly leading with well positioned units in muta-ling-baneling packs can allow a player to run over a minefield with near impunity. Use it if you can. It's a cool tactic.

And that's all for now.
Comments? Questions? Concerns?

Best of luck to you all,
Lone

MOD EDIT:
Here is Morrow's version from: http://www.teamliquid.net/forum/viewmessage.php?topic_id=403618&currentpage=3#49
On March 18 2013 14:15 MorroW wrote:
how widow mine works
they lock onto a target. first one who enter within 5 range OR best unit (which is basically the closest unit to the widow mine)
once they lock into a target it begins channeling for 1.5 seconds (ingame)

if the unit leaves the 5 range, dies or player manually switches target during the channeling period - the widow mine repeats the process


so this is why mines sometimes dont attack, sometimes kill terran and sometimes kill zerg
so lets say you run in with zerglings against marines and a widow mine. the widow mine locks onto the first zergling who enters.
if the zergling dies to marines, it changes target and has to wait another 1.5 sek, if that ling dies to marines it changes target etc. so it appears not to be attacking at all.
if the zergling runs past the widow mine, behind the marines for example it switches target as well (the target has to be within 5 range the entire lockdown process)

as terran
so in a fight, you basically as terran ideally want to switch targets between the zerglings until the banelings enter range and then you target the bane and let the mines be.
second option is to stay with the marines, burst down as many lings as you can, and hopefully (and probably) you will kill all zerglings which were targetted automatically by the widow mines before they finish channeling and then banelings enter and you target the mines onto the banes

as zerg
as a zerg player, you know that your first zerglings will be targetted, so use your frontal line in move command behind the terran army and attack with the rest of your zerglings normally. if you do this just right (and terran doesnt) the mines will all fire on your lings that are behind his bio army and kill everything he got


widow mines appear random at the first glance of it. but the more you play around with them the more you realize how much you (as terran or zerg) can manipulate them and make them do exactly what you want them to. its not a user friendly unit at all because of how it can completely backfire using widow mines where as a siege tank you know will do a certain amount of damage. things like this is really beautiful and what is making bw a very different game from sc2. in bw there were tons of "OP" units that crushed your opponent or did close to nothing or killed yourself where as in sc2 its much more predictable whats expected of a unit because the complexity of it its not very deep

i think the widow mines are slightly too strong right now. but if your a zerg reading this i hope it helped abit how to make the widow mines turn against the terran instead of raping everything you got

reikai
Profile Joined January 2011
United States359 Posts
March 19 2013 14:04 GMT
#2
+ Show Spoiler +
This explains a lot of the game on Daybreak, especially the battle in the the bottom middle base where Day[9] was even confused as to why Life's army took almost no damage.

Back to bio-tank? :[
Et Ducit Mundum Per Luce. :T:
Surili
Profile Blog Joined March 2011
United Kingdom1141 Posts
March 19 2013 14:12 GMT
#3
Could you possibly make an image to help me understand? I'm pretty dim.
The world is ending what should we do about it?
SongMeister
Profile Joined May 2012
United States20 Posts
March 19 2013 14:26 GMT
#4
damn lone, this is some serious stuff.... very nice work!
StagaDish
Profile Joined February 2013
United States9 Posts
March 19 2013 14:26 GMT
#5
On March 19 2013 23:12 Surili wrote:
Could you possibly make an image to help me understand? I'm pretty dim.


^
This sounds like very useful information, but also very confusing for ppl with low math skillz. An image is a cool idea. Also video showing how this works (or when it doesn't - like when unit moves too slow or in the wrong path over mines).

Might be a lot to ask, but it sounds like you're on to something really important here! Put some effort so everybody could understand it easily :D

gl!
And thanks in advance
Practice Makes Perfect
AveSharia
Profile Joined April 2011
United States62 Posts
Last Edited: 2013-03-19 14:38:10
March 19 2013 14:33 GMT
#6
Given that, the very close units will already be halfway over the mine's radius.


I think that's the most important point in the whole piece. Lead with lings, and the even the slower stuff that follows won't get hit.

Also, if I'm not mistaken, the Flash v Life engagement occurred off creep (http://bcove.me/gt7scsrw, 13ish minutes*). So this statement:

He realized that if he attacked from the correct angle, he could get mines to lock onto Zerglings which would not pass within 2 range of the burrowed mines.


...seems a bit misleading. The range should probably say 3.5.

* EDIT: The mines were actually at the edge of the creep, so the effective radius is going to fall between 2 and 3.5.
jrkirby
Profile Blog Joined August 2010
United States1510 Posts
Last Edited: 2013-03-19 17:36:07
March 19 2013 14:33 GMT
#7
This is huge! A lot of people might have thought the widow mine is OP, but if you can micro against it like this, that has huge implications for all the terran matchups.
hzflank
Profile Joined August 2011
United Kingdom2991 Posts
March 19 2013 14:34 GMT
#8
On March 19 2013 23:12 Surili wrote:
Could you possibly make an image to help me understand? I'm pretty dim.


I cannot make an image, but I can explain it without any math.

A widow mine picks a target that comes within it's range. If it is a slow moving target it will fire at it. If it is a fast moving target it will only fire if the targeted unit gets very close to the mine. A widow mine can only have on target at a time.
mvdunecats
Profile Joined December 2011
United States102 Posts
March 19 2013 14:46 GMT
#9
On March 19 2013 23:26 StagaDish wrote:
Show nested quote +
On March 19 2013 23:12 Surili wrote:
Could you possibly make an image to help me understand? I'm pretty dim.


^
This sounds like very useful information, but also very confusing for ppl with low math skillz. An image is a cool idea.

No images to contribute, but imagine a circle. Now draw a line segment that is inside the circle. The longest line segment that you can have inside the circle is one that crosses through the center. The further the line is from the center, the shorter the line segment will be. The extreme case for the shortest line segment possible is a line that is tangent to the circle.

The widow mine is the center of that circle. People will instinctively think that they need to stay outside that circle to avoid damage from the widow mine. But because of the arming delay for the widow mine's attack, you can enter that circle as long as you get back out fast enough.

So going back to that mental image of line segments going through the circle. How quickly you can move from one end of the line to the other depends on how long the line is (the longer the line, the longer it takes to move that far) and how fast the unit is (a faster unit can cross a fixed length line in less time than a slower unit). A faster unit can run closer to the widow mine and still be safe.
Ahli
Profile Joined May 2012
Germany355 Posts
Last Edited: 2013-03-19 15:12:20
March 19 2013 14:50 GMT
#10
The widow mine has a unit radius of 0.5 that is added to the range. Because the widow mine is burrowed, units can move across it. So it's actual range is 5.5.
AhliSC2@Twitter - GameHeart Observer UI - "HomeStoryCup XX" extension mod fixes WCS GameHeart's small bugs, adds a lot of new features -
Chernobyl
Profile Joined March 2011
Brazil143 Posts
March 19 2013 14:50 GMT
#11
Very good post.

Is far better than simply qq about a new unit.

For me, hots is amazing, and the widow mine is a very entertaining unit.
Rannasha
Profile Blog Joined August 2010
Netherlands2398 Posts
March 19 2013 14:59 GMT
#12
Fear my mad MS Paint skills:
[image loading]
The black dot is the w-mine, the black circle the edge of the trigger range (radius 5). Suppose a unit passes by over the dark gray line, then the light grey line indicates the "effective radius".

The numbers in the first post are the maximal effective radii for various units to still trigger the mine (that is, the mine fires before the unit exits the radius 5 circle). The faster the unit, the closer it can pass by the w-mine without getting hit.
Such flammable little insects!
Ahli
Profile Joined May 2012
Germany355 Posts
Last Edited: 2013-03-19 15:10:58
March 19 2013 15:09 GMT
#13
I made an Example image with Speedlings on creep not activating mine.

The ling in the south enters the range first, but leaves it. This allows the rest of the speedlings to directly travel over the mine.
AhliSC2@Twitter - GameHeart Observer UI - "HomeStoryCup XX" extension mod fixes WCS GameHeart's small bugs, adds a lot of new features -
Miotonir
Profile Joined March 2011
Poland66 Posts
March 19 2013 15:10 GMT
#14
This is somewhat true when the target is moving quickly but for targets that are slow the effectiveness of the mine is higher... so for example a stimmed marine might dodge the bullet , but non stimmed will not altho going trough same path ... It is perfect then for all matchups because a ling has higher chance of avoiding the mine ... while a zelot has lower since it has higher hp and slower movement speed.
ensign_lee
Profile Joined June 2010
United States1178 Posts
March 19 2013 15:38 GMT
#15
Holy crap. What a high quality post.
Arghmyliver
Profile Blog Joined November 2011
United States1075 Posts
March 19 2013 15:39 GMT
#16
Wow dude - that's some sick mathematical insight! As a calculus veteran I say - major props!
Now witness their attempts to fly from tree to tree. Notice they do not so much fly as plummet.
_fool
Profile Joined February 2011
Netherlands658 Posts
March 19 2013 15:42 GMT
#17
What's really cool about this post is that even without grasping the full math, I immediately got your point. Good job OP!
"News is to the mind what sugar is to the body"
Pufftrees
Profile Joined March 2009
2449 Posts
March 19 2013 15:44 GMT
#18
Simple elegant math leading to excellent insights! What is this the 15th century?

Nice job
Chance favors the prepared mind.
StagaDish
Profile Joined February 2013
United States9 Posts
March 19 2013 15:51 GMT
#19
Lone, we might have to call you "The DeWidower" from now on...
Practice Makes Perfect
Targe
Profile Blog Joined February 2012
United Kingdom14103 Posts
March 19 2013 15:53 GMT
#20
Awesome! Maths!
Nice job on interpreting it, I wouldn't have thought to work out a radius that is the closest you can get without activating, I guess the counter to this strategy is to manually target the mines on units further from the mine (after the initial ling).
11/5/14 CATACLYSM | The South West's worst Falco main
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